Investigation of half metallic properties of Tl2Mo(Cl/Br)6 double perovskites for spintronic devices

The manipulation of electronic device characteristics through electron spin represents a burgeoning frontier in technological advancement. Investigation of magnetic and transport attributes of the Tl2Mo(Cl/Br)6 double perovskite was performed using Wien2k and BoltzTraP code. When the energy states between ferromagnetic and antiferromagnetic conditions are compared, it is evident that the ferromagnetic state exhibits lower energy levels. Overcoming stability challenges within the ferromagnetic state is achieved through the manipulation of negative ΔHf within the cubic state. The analysis of the half metallicity character involves an analysis of band structure (BS) and DOS, elucidating its mechanism through PDOS using double exchange model p–d hybridization. The verification of 100% spin polarization is confirmed through factors such as spin polarization and the integer value of the total magnetic moment. Furthermore, the thermoelectric response, as indicated by the ratios of thermal-electrical conductivity and ZT, underscores the promising applications of these compounds in thermoelectric device applications.


Introduction
Spintronics, a new research area at the intersection of physics and electronics, has become particularly interesting owing to its possible inuence on the development of novel types of electronic devices based on electron spin (their intrinsic property). 1nlike in traditional electronics, which mainly rely on electron charges for data handling and storage, spintronics employs the electron's spin degree of freedom, which results in the appearance of electronic devices with novel and enhanced functionalities. 2 Spintronics is actually a branch of electronics based on one of the fundamental concepts, namely half metallicity, which is a special property of materials characterized by the fact that they have different conductive properties for electrons with different spin orientations.4][5] This property provides completely novel capabilities for controlling and manipulating the magnetic moment of itinerant electrons and opens new avenues for utilizing this spin dependence in various devices.The investigation of half-metallicity in spintronics has opened up new avenues for the fabrication of spin-based electronic devices such as spin valves, magnetic tunnel junctions and spin transistors, which depend on differentiating and manipulating the spin-polarized currents. 6In addition, the design and production of half-metallic materials in spintronics directly affect spin-dependent phenomena such as colossal magneto-resistance and tunnel magneto-resistance, which are limiting factors in high-density magnetic data storage and spintronic memory devices. 7Researchers have targeted the inherent traits of the half metallic substances and intend to outdo the outmoded limitations in electronic devices in terms of power consumption, speed and scalability to ready the juncture for the forthcoming spintronic innovations.Concurrently, the quest for new materials has made this discovery of double perovskites, a very diverse group of compounds famed for their versatile properties. 8In this scenario, the origins of spintronics, half-metallicity, and double perovskites are of great importance, affecting material design and technological innovation.
Besides the emergence of half-metallic materials, the class of compounds known as double perovskite has gained attention because of its unique properties of electronic and magnetic capability due to its complex crystal structure and various cationic congurations.The perovskite structure is

RSC Advances
PAPER characterized by a simplied addressing by the general formula.A 2 BB 0 O 6 can be regarded as a versatile framework for the investigation of a broad spectrum of physical phenomena and the design of material properties through composition engineering. 9Double perovskites, a subgroup of perovskite materials featuring the simultaneous occupation of two cations at the B site, display various high-order electronic structures with a rich phase space that can lead to numerous electronic transport characteristics.Such engineering would yield a structure with mutable electronic band structures through approaches including, but not limited to, band engineering, strain engineering, and doping.In addition, the functionality of the transition metal nodes of the perovskite lattice leads to signicant phase space, and the existence of electronic phenomena, such as colossal magnetoresistance and multiferroicity, is possible.Additionally, the intriguing interplay between phonon properties and electronic states in double perovskite material provides a way to explore novel phenomena that may enhance the properties of the thermoelectric ZT.The essence of the thermoelectric function of double perovskites is the complex relationship between the electronic structure, charge transport, and phonon scattering mechanisms. 10The band engineering possibilities from the dual-cation arrangement ensure that the electronic states can be manipulated, and their mobility is improved, thereby, in the process, boosting the thermoelectric efficiencies. 11Furthermore, particular d-electrons of transition metal ions and conducting oxygen p-orbitals also play a role in the complex electronic behavior of the materials; this means that such compounds have ideal properties for further development of thermoelectric properties. 12umerous researchers have allocated their ndings specically to studying the double perovskite group due to the intriguing thermoelectric properties of this material.Mahmood et al. studied the ferromagnetic thermoelectric response of K 2 Z(Cl/Br) 6 (Z = Ta, W, Re), which is related to its application in spintronics and energy.Their investigation delivered an in-depth description of the features of these materials when comparing them in terms of their different possible uses in future technological developments.Mahmood et al.'s ndings provide a signicant impetus for research in materials for spintronic and energy applications. 13Alburaih et al. presented a theoretical investigation, relying thoroughly on DFT calculations, of vacancyordered single-crystalline K 2 TcZ 6 (Z = Cl, Br) systems searching owing to their suitable characteristics for spintronic applications.Their work focused on the electronic structure and magnetic response in the studied composition and provided a basis for the development of new spintronic devices and data storage. 14In the research by Mahmood et al. (2022), the impact of 5d electrons on half metallic ferromagnetic behavior and conduction of Cs 2 Z(Cl/ Br) 6 (Z = Os, Ir) for devices in spintronics was explored. 15The study featured a comprehensive analysis of the behavior of these materials, which served as the basis for the development of novel spintronic devices.The authors explored the relationship between 5d electrons and their proprieties in detail, providing contributions that can be valuable for materials.Their ndings emphasize that the Cs 2 Z(Cl/Br) 6 (Z = Os, Ir) compound might play a key role in the development of spintronics, which again makes them theoretically critical for future science and technology.The molecules Mo and Tl provide remarkably strong spins used in the devices to store and process information using spins.As far as the tunability of Tl and Mo and the possibility of application in devices with the magnetization effect are concerned, magnetronics could be a crucial eld.With our calculations, we are condent that Tl 2 Mo(Cl/Br) 6 will denitely be the best composition in spin-based technology.Perovskites with halide composition exhibit applications in several spintronic gadgets, including magnetic memory, spin valves, and spin orbit applications due to the unique magnetic and electrical tunability of the combination.Spintronics has been performing very well, and further advancements in this area will potentially command various possibilities and highly adaptive spintronic device functionalities.The principal objective of the present investigation is to acquire a more comprehensive understanding of the characteristics of Tl 2 Mo(Cl/Br) 6 , covering aspects such as structural, electronic, elastic, magnetic, and transport properties.

Computational methodology
The stability of a material's structure is crucial because it governs numerous physical attributes.In this study, Tl 2 Mo(Cl/ Br) 6 was analyzed using a DFT-based FP-LAPW approach implemented using Wien2k code. 16Ground-state energies were computed using the PBE-sol approximation, with adjustments made to accurately determine bandgaps through the mBJ potential. 17Notably, PBE-sol, a modied version of PBE, incorporates different constraints, offering improved accuracy, particularly for heavy metal systems related to PBE.The TB-mBJ potential, known for its precision akin to HSE06, was employed for electronic BS and DOS computations, alongside consideration of spin-orbit coupling. 18,19To ensure convergence, a Kmesh of 2000 k-points (12 × 12 × 12) was utilized and later increased to 20 × 20 × 20 for thermoelectric calculations.Parameters such as (muffin-tin radius) R MT × K max (K-vector), ' max (angular momentum vector) and G max (Gaussian factor) were carefully selected for accuracy, with computed results converging to the order of 10 −3 mRy.Transport response was estimated utilizing the BoltzTrap code, providing an inclusive analysis of the material's properties. 20

Structural analysis
The optimization of energy release from compounds with Fm 3m (no.225) space group in cubic phase and determination of ground-state parameters were conducted using the Birch- Murnaghan equation of states (Table 1). 21 The Mo atoms occupies the center of the octahedra, encircled by six Cl/Br atoms, while the Mo atoms are also present at the face centers and corners. 22Wyckoff positions for Tl (8c), Mo (4a), and Cl/Br (24e) were utilized for structure generation and optimization.Through the replacement of Cl with Br, atomic radii increase, consequently enlarging the lattice constant in the range of 9.95-10.54Å and inter-atomic distance, thus reducing material density and solidness, and leading to a decrease in bulk moduli (B) from 43.75-35.95GPa. 23The same type of variation in the lattice constant has also been observed by Mahmood et al. in Cs 2 ReCl/Br 6 double perovskites. 11The considerable bulk modulus of Tl 2 MoBr 6 suggests greater stiffness compared to Tl 2 MoCl 6 .Energy plots against volume in the ferromagnetic (FM) and anti-ferromagnetic (AFM) phases, as displayed in Fig. 2, reveal higher energy release in the FM state, indicating its greater favorability.Furthermore, energy formation was computed to evaluate thermal stability using the following equation: 24 where E Total denotes the total energy of double perovskites; E Tl , E Mo , and E Cl/Br denote energies of Tl, Mo, and Cl/Br, respectively; l denotes the number of Tl; m denotes the number of Mo and n denotes the number of Cl/Br atoms. 25The DH f for Tl  provides additional insight into directional characteristics, where isotropic materials possess a unit value and anisotropic materials exhibit a value less than unity (Table 2). 31

Elastic anisotropy
Elastic anisotropy represents the signicant physical characteristics of a material, indicating variations in physical and chemical properties with directional changes. 32Isotropic materials maintain reliable characteristics irrespective of measurement directions, exhibiting identical performance values in all directions.Fig. 3

Electronic properties
To elucidate the electronic behavior of Tl 2 Mo(Cl/Br 6 ), we generated visual representations of band structures (BS) in Fig. 4, and the density of states (DOS) is depicted in Fig. 5 and 6.
The band structures unveil state presence at Fermi level (E f )   , the E f is notably absent at that position, as depicted in Fig. 5 and 6.Consequently, the investigated halides exhibit complete spin polarization (P = 1). 38urthermore, to give an inclusive insight into ferromagnetism, the density of states (DOS) is graphically illustrated in Fig. 5 and 6.An analysis of the total density of states (TDOS) reveals that the up ([) spin channel exhibits characteristics of direct bandgap semiconductors along the G symmetry direction, whereas the down (Y) spin channel demonstrates an insulating nature.Consequently, the interplay between semiconductor and insulator responses facilitates electron exchange, thereby inducing ferromagnetic characteristics.The basic driver of ferromagnetism in Tl 2 MoCl 6 and Tl 2 MoBr 6 stems from the individual electronic states of Mo, Tl, and Cl/Br hybridization.Specically, the d-state of Mo splits into t 2g and e g states of Mo upon encountering the octahedral and tetrahedral environments of halide atoms. 39The e g state shis to low energy levels, whereas the t 2g state ascends to high energy levels.Among these, the t 2g state, comprising d xy , d yz , and d zx orbitals, exhibits a linear trend and signicantly contributes to hybridization, whereas the e g state, comprising d z 2 and d x 2 −y 2 orbitals, displays Furthermore, a hybridization zone between the t 2g states of Mo and Cl's 3p states emerges in the −2.2 to −4.8 eV energy range although this range is not pertinent to our analysis. 41Notably, signicant hybridization is observed between Mo's e g and Cl's 3p states in the vicinity of the CB edge.In the down (Y) spin conguration, hybridization arises among Mo's t 2g and Cl's 3p states in VB and CB, respectively.However, the core region witnesses negligible participation in the hybridization process, as shown in Fig. 5. Similarly, robust hybridization is evident between Mo's t 2g and 4p states of Br, as illustrated in Fig. 6.Additionally, reasonable hybridization between Mo's e g and Br's 4p states is observed in the conduction band.In the down (Y) spin conguration, hybridization arises among Mo's t 2g , Br's 4p states, and Tl's 6s states in VB and CB.We also computed phonon dispersion curves for both investigated materials, revealing that no imaginary mode is observed for Tl 2 Mo(Cl/Br) 6 (see Fig. 7).The positive value of the phonon frequency for both materials indicates that they are dynamically stable in the given temperature range.

Magnetic properties
Understanding ferromagnetism relies signicantly on the splitting of VB and CB edges, particularly concerning the interactions between s and d orbitals as well as p and d orbitals. 42These orbital interactions, denoted as s-d and pd couplings, respectively, are delineated based on the average magnetic moments of Mo within the unit cell.The energy discrepancy between the up ([) and down (Y) spin congurations at the CB edge (denoted as E c ) predominantly reects the inuence of s-d coupling.Conversely, at the valence band edge, this energy difference (denoted as E V ) encompasses contributions from p-d coupling.The specics of these interactions are further expounded through the elucidation of exchange constants as follows: where x represents the concentration of Mo and hSi denotes its average magnetic moment. 43The presence of negative values for N o b indicates high level of attraction towards down (Y) spin conguration within the exchange mechanism, resembling the characteristics of ferromagnetism, akin to exchange energy D(pd), as outlined in Table 4.The transition of electrons from the down (Y) spin to up ([) spin conguration, coupled with robust hybridization between the d states of Mo, 3p state of Cl, and Br 4p-states, introduces both orbital and spin magnetic moments, highlighting their signicance in spintronic devices.Detailed magnetic moment data for individual elements Tl, Mo, and Cl/Br, as well as compounds Tl 2 Mo(Cl/Br) 6 , are provided in  Table 5. 44 The presence of magnetic moments on nonmagnetic elements arises from robust hybridization and SOC among the d state of Mo, 3p state of Cl and Br-4p state, underscoring the pivotal contribution of Mo's d state in spintronic applications.Furthermore, Table 5 displays both the total and individual magnetic moments for Tl 2 Mo(Cl/Br) 6 .The integral gures of total magnetic moments signify complete spin-polarization of the composition under investigation.The predominant source of magnetic moments stems from the Mo-d state.Strong hybridization particularly results in the transfer of the magnetic moments from the Mo site to Tl and Cl/Br. 45

Thermoelectric properties
In recent years, noteworthy attention has been paid to the potential of a thermoelectric material to convert thermal energy into electrical energy across various applications. 46This phenomenon, known as the thermoelectric effect, relies on the transfer of charge movement to generate a heat gradient, thereby creating a potential difference.The thermoelectric properties of Tl 2 Mo(Cl/Br) 6 were examined utilizing the Boltz-TraP code with diverse parameters, as presented in Fig. 8(a-f).Within the BoltzTraP simulation, the relaxation time, set at 10 −14 s, denotes the average duration between successive collisions within the system.Electrical conduction induced by charge carriers is determined by evaluating s/s. 47As depicted in Fig. 8(a), the transition from Cl to Br prompts a rapid escalation in s/s, which is attributable to the heightened presence of free electrons transitioning thermally from valence to the conduction band.At 200 K, s/s measures 2.5 × 10 19 for Tl 2 MoCl 6 and  2.7 × 10 19 (U m s) −1 for Tl 2 MoBr 6 .Analogous trends persist at 800 K.The increase in conductivity following the substitution of Cl with Br can be ascribed to the larger ionic size and the augmented contribution of free carriers.However, as the temperature increases, conductivity decreases potentially due to heightened resistance experienced by free carriers amidst thermal agitation at higher temperatures.Thermal conductivity (k e /s) represents the carrier's conduction because of heat, with only the electronic component calculated while disregarding lattice contributions.For Tl 2 MoCl 6 , thermal conductivity escalates from 1.0 × 10 14 at 200 K to 1.42 × 10 14 (W m −1 K −1 s −1 ) at 800 K, and a similar trend is observed for Tl 2 MoBr 6 , as illustrated in Fig. 8(c).The optimal performance is indicated by minimizing k e /s, as observed from k/s.The electronic to thermal (k/s) conductivity ratio is in the order of 10 −6 , 48 emphasizing their signicance for thermoelectric applications due to their lower k/s values related to s/s.The Seebeck coefficient (S) serves as a crucial gauge of potential gradients and is charted against the temperature.The polarity of S values, negative or positive, delineates whether electrons or holes predominate as charge carriers.For temperatures ranging from 200 to 800 K, Fig. 8(c) illustrates the uctuation in S. Notably, for Tl 2 Mo(Cl/Br) 6 , the S value increases as the temperature increases potentially due to disparities in energy magnitude among the upper VB and E f , 49 as illustrated in Fig. 8(c).The magnetic response of materials is characterized by their susceptibility, typically around 10 −9 for semiconductors.At 200 K, Tl 2 Mo(Cl/Br) 6 exhibits susceptibility of 4.4 × 10 −9 and 3.6 × 10 −9 m 3 mol −1 , respectively; then, its value decreases at 800 K, which is potentially inuenced by thermal effects on electron spin movement, as depicted in Fig. 8(d).In Fig. 8(d), sS 2 /s, termed the power factor (PF), representing the thermoelectric potency of materials, is drawn against the temperature.The behavior of s/s and PF aligns closely due to the extremely conductive response of a material.As the temperature increases, PF diminishes upon substituting Cl with Br. 50Comparative analysis reveals that PF for Tl 2 MoCl 6 surpasses that of Tl 2 MoBr 6 due to the predominance of n-type carrier contributions over p-type carriers. 51The gure of merit (ZT), illustrated in Fig. 8

Conclusion
In the current study, a thorough analysis of the half metallic ferromagnetic and thermoelectric responses of Tl 2 Mo(Cl/Br) 6 double perovskites was conducted to explore their perspectives in spintronics and thermoelectric applications.Initially, structural optimization was performed in the ferromagnetic (FM) and anti-ferromagnetic (AFM) phases, conrming the stability of the FM phase.Additionally, the formation energies of Tl 2 -MoCl 6 and Tl 2 MoBr 6 are −1.44 and −1.88 eV, respectively, indicating thermodynamic stability.The 100% spin polarization was conrmed through spin-polarized electronic DOS, revealing underlying hybridization and fractional magnetic moments alongside higher T c .Exchange energies and valence electron hybridization further conrmed the ferromagnetic response attributed to electron spin instead of clustering.Quantum connement predominantly inuenced negative exchange coefficient values and p-d exchange energy.Moreover, the calculations of S unveiled the existence of p-type semiconducting characteristics in Tl 2 Mo(Cl/Br) 6 .The notably higher ZT at 800 K observed as 0.33 and 0.26 for Tl 2 MoCl 6 and Tl 2 -MoBr 6 , respectively, suggested their comparative suitability for thermoelectric device application.

Fig. 1
illustrates unit cells in both ball-stick (le) and polyhedral (right) formats, showcasing atomic arrangement and geometric conguration, respectively.Within MoCl/Br 6 octahedra, the Tl atom lls vacancies, which exhibit 12-fold coordination with Cl/Br atoms, resulting in individual octahedra being distinct from the others.
within spin-up ([) conguration, exhibiting characteristics akin to direct bandgap semiconductors.Conversely, within the down (Y) spin channel, the E f resides in the band-gap, indicating insulating properties.37This transition of states between the up ([) and down (Y) congurations underscores the manifestation of the ferromagnetic character.It is imperative to note that achieving complete 100% spin-polarization serves as a fundamental prerequisite for half-metallic FM behavior.Hence, spinpolarization is quantitatively assessed via the equationP = (N Y (E F ) − N [ (E F ))/(N Y (E F ) + N [ (E F )),where N Y (E F ) denotes the DOS in the down (Y) spin and N [ (E F ) denotes the DOS at E f in the up ([) spin conguration.Notably, within the up ([) spin conguration, states are situated precisely at E f , whereas in the down (Y) spin conguration

Fig. 5
Fig. 5 Total and partial DOS for Tl 2 MoCl 6 with Tl, Mo and Cl atoms in spin up ([) and down (Y) spin configurations.

Fig. 6
Fig. 6 Total and partial DOS for Tl 2 MoBr 6 with Tl, Mo and Br atoms in spin up ([) and down (Y) spin configurations.

Table 5
Total and local values of magnetic moments for Tl 2 Mo(Cl/Br) 6 52), is expressed by ZT = S 2 s/kT.A high ZT value at low-temperature values indicates minimal thermal conductivity alongside a small S and higher s/s.The relationship for ZT demonstrates a direct proportional trend between k e /s and s/s against temperature.The curve for Tl 2 MoBr 6 is lower, attributed to slightly greater S and high k e /s compared to the Tl 2 MoCl 6 curve.The maximum ZT values are 0.33 for Tl 2 -MoCl 6 and 0.26 for Tl 2 MoBr 6 at 800 K.52